What Hoeffding's inequality bounds: tail probability of sum of bounded random variables

What Chebyshev's inequality says: P(|X-μ| ≥ kσ) ≤ 1/k²

Chebyshev's inequality states that the probability of a random variable deviating from its mean by at least k standard deviations is less than or equal to 1/k²

Mutual information I(X;Y) = H(X) - H(X|Y) = H(Y) - H(Y|X)

Mutual information measures dependence between variables X and Y

What importance sampling does: reweights samples from proposal to estimate target expectation

Importance sampling reweights samples from a proposal distribution to approximate the expectation of a target distribution

Shannon's channel capacity: C = B log₂(1 + S/N) bits per second

Shannon's formula: C = B log₂(1 + S/N) defines channel capacity in bits/s

What mixup does: trains on convex combinations of pairs: x̃=λx_i+(1-λ)x_j

Trains on convex combinations of pairs: x̃=λx_i+(1-λ)x_j represents a weighted average of two points in a convex set

How does the concept of homotopy type theory (HoTT) enable the unification of homotopy theory and higher category theory in mathematical foundations?

HoTT unifies homotopy theory and higher category theory by using types as mathematical objects, enabling homotopical and categorical structures to coexist